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Cubic reciprocity and generalised Lucas-Lehmer tests for primality of 
Authors:
Pedro Berrizbeitia and T. G. Berry
Journal:
Proc. Amer. Math. Soc. 127 (1999), 1923-1925
MSC (1991):
Primary 11A51, 11Y11
Posted:
February 18, 1999
MathSciNet review:
1487359
Full-text PDF Free Access
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Abstract: Cubic reciprocity is used to derive primality tests analogous to the Lucas-Lehmer test for integers of the form  . The test for  is a minor improvement on a test derived by Williams by other means; the test for  seems to be new.
- [G]
Andreas
Guthmann, Effective primality tests for integers of the forms
𝑁=𝑘⋅3ⁿ+1 and
𝑁=𝑘⋅2^{𝑚}3ⁿ+1, BIT
32 (1992), no. 3, 529–534. MR 1179238
(93h:11008), http://dx.doi.org/10.1007/BF02074886
- [IR]
Kenneth
F. Ireland and Michael
I. Rosen, A classical introduction to modern number theory,
Graduate Texts in Mathematics, vol. 84, Springer-Verlag, New York,
1982. Revised edition of Elements of number theory. MR 661047
(83g:12001)
- [R]
Michael
I. Rosen, A proof of the Lucas-Lehmer test, Amer. Math.
Monthly 95 (1988), no. 9, 855–856. MR 967346
(89i:11011), http://dx.doi.org/10.2307/2322904
- [W1]
H.
C. Williams, The primality of 𝑁=2𝐴3ⁿ-1,
Canad. Math. Bull. 15 (1972), 585–589. MR 0311559
(47 #121)
- [W2]
H.
C. Williams, A note on the primality of 6^{2ⁿ}+1 and
10^{2ⁿ}+1, Fibonacci Quart. 26 (1988),
no. 4, 296–305. MR 967648
(89i:11013)
- [W3]
H.
C. Williams, A class of primality tests for trinomials which
includes the Lucas-Lehmer test, Pacific J. Math. 98
(1982), no. 2, 477–494. MR 650024
(83f:10008)
- [G]
- A. Guthmann. Effective primality tests for
 and  . BIT 32 (1992) 529-534. MR 93h:11008
- [IR]
- K. Ireland and M. Rosen. A classical Introduction to Modern Number Theory. Springer-Verlag, Berlin, 1982. MR 83g:12001
- [R]
- M. Rosen. A proof of the Lucas-Lehmer test. Amer. Math. Monthly 95 (1988) 855-856. MR 89i:11011
- [W1]
- H. C. Williams The primality of
 . Can. Math. Bull. 15 (1972) 585-589. MR 47:121
- [W2]
- H. C. Williams. A note on the primality of
 and  . Fibonacci Quart. 26 (1988) 296-305. MR 89i:11013
- [W3]
- H.C. Williams A class of primality tests for trinomials which includes the Lucas-Lehmer test. Pacific J. Math 98 (1982) 477-494. MR 83f:10008
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Additional Information
Pedro Berrizbeitia
Affiliation:
Departamento de Matematicas Puras y Aplicadas Universidad Simón Bolívar Caracas, Venezuela
Email:
pedrob@usb.ve
T. G. Berry
Affiliation:
Departamento de Matematicas Puras y Aplicadas Universidad Simón Bolívar Caracas, Venezuela
Email:
berry@usb.ve
DOI:
http://dx.doi.org/10.1090/S0002-9939-99-04786-3
PII:
S 0002-9939(99)04786-3
Received by editor(s):
September 24, 1997
Posted:
February 18, 1999
Communicated by:
David E. Rohrlich
Article copyright:
© Copyright 1999 American Mathematical Society
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